arithmatic

Question

the LCM of the two numbers is six times their HCF .If the difference between the LCM and HCF is 60 and one of the numbers  is 36 find the other number

Answer 1

One of the numbers is 36 = 2*2*3*3.

The LCM (Least Common Multiple) of 36 and another number is 36x (where x includes the remaining factors from the other number).

 

“The LCM is six times the HCF,” so the HCF (Highest Common Factor) is 36x/6 = 6x.

 

“The difference between the LCM and HCF is 60” means   36x - 6x = 60

                30x = 60

                     x = 2

 

Check:  The LCM  (36x) is 72 and is six times the HCF (6x) of 12.  And 72-12=60.

 

The numbers are:

      2*2*3*3 = 36     (given)

      2*2*2*3 = 24     (factor of x=2 included; only one 3 because of HCF=12)

Answer 2

LCM=6*GCF

LCM-GCF=60

substitute

6*GCF-GCF=60

5*GCF=60

GCF=60/5

GCF=12

LCM=6*GCF=72

In mathematics the product of the two numbers divided by the LCM gives you the GCF and the product of the two numbers divided by the GCF gives you the LCM.

In mathematics the product of the LCM and the GCF divided by one of the numbers gives you the other number.

12*72=864

864/36=24

24 is the other number